For your reference, this is the rubric I will use to grade your project:

Numerical Methods Project (100 points total)

Part I (25 points): Use technology to approximate the solution to your Initial Value Problem using Euler’s Method, the Improved Euler’s Method, and the Runge-Kutta Method.

  • (1 point) Appropriate technology selection
  • Euler’s Method implementation:
    (2 points) Displays all points (xi,yi)
    (2 points) Displays slope k at each stage
    (4 points) Calculates correctly
  • Improved Euler’s Method implementation:
    (2 points) Displays all points (xi,yi)
    (2 points) Displays values of k1,k2 at each stage
    (4 points) Calculates correctly
  • Runge-Kutta Method implementation:
    (2 points) Displays all points (xi,yi)
    (2 points) Displays values of k1,k2,k3,k4 at each stage
    (4 points) Calculates correctly

Part II (25 points). Find the exact solution to the Initial Value Problem and use it to determine the value requested in the problem. Round your answer to 8 decimal places.

  • (15 points) Exact solution of differential equation
  • (10 points) Value at requested point (8 decimals)

Part III (25 points). Compare the exact value obtained in Part II to the three numerical approximations obtained in Part I. How many correct decimal digits did each method produce? Which method was the most accurate?

  • (15 points) Compare value from Part II to the three numerical approximations.
  • (5 points) How many correct digits did each method produce?
  • (5 points) Which method was the most accurate?

Part IV (25 points). Reflection. Write one or two paragraphs (minimum 300 words) responding to the following. Leave your response to this part as a comment on this post.

  • (5 points) 300 words min.
  • (4 points) Describe your project and how it works.
  • (4 points) Describe the process of building your project (technology challenges?)
  • (4 points) Why do we need numerical methods?
  • (4 points) Why is this assignment included in the class?
  • (4 points) Please include a link to your project or file